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Given that the roots of the equation 24...

Given that the roots of the equation ` 24x^(3) - 26x^(2) + 9x - 1 = 0` are in HP , find them

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To find the roots of the equation \( 24x^3 - 26x^2 + 9x - 1 = 0 \) given that the roots are in Harmonic Progression (HP), we can follow these steps: ### Step 1: Understand the relationship of roots in HP If the roots \( a, b, c \) are in HP, then their reciprocals \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in Arithmetic Progression (AP). This means: \[ \frac{2}{b} = \frac{1}{a} + \frac{1}{c} \] This can be rearranged to: ...
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